4. A year 12 student wishes to study at a Welsh university. For a randomly chosen year between 2000 and 2017 she collected data for seven universities in Wales from the Complete University Guide website. The data are for the variables:

• 'Entry standards' - the average UCAS tariff score of new undergraduate students;
• 'Student satisfaction' - a measure of student views of the teaching quality at the university taken from the National Student Survey (maximum 5);
• 'Graduate prospects' - a measure of the employability of a university's first degree graduates (maximum 100);
• 'Research quality' - a measure of the quality of the research undertaken in the university (maximum 4).
  1. Pearson's product-moment correlation coefficients, for each pairing of the four variables, are shown in the table below.
     Discuss the correlation between graduate prospects and the other three variables.

Calculate the equation of the least squares regression line to predict 'Entry standards'( \(y )\) from 'Research quality'( \(x\) ), given the summary statistics: $$\sum x = 22.24 , \sum y = 2522 , S _ { x x } = 1.0542 , S _ { y y } = 20193.5 , S _ { x y } = 122.72 .$$

The data for one of the Welsh universities are missing. This university has a research quality of 3.00 . Use your equation to predict the entry standard for this university.